Exponential smoothing additive

*The author of this computation has been verified*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Tue, 28 Dec 2010 11:59:51 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293537462ypx8bhbmhfvwhta.htm/, Retrieved Tue, 28 Dec 2010 12:57:46 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293537462ypx8bhbmhfvwhta.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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621 587 655 517 646 657 382 345 625 654 606 510 614 647 580 614 636 388 356 639 753 611 639 630 586 695 552 619 681 421 307 754 690 644 643 608 651 691 627 634 731 475 337 803 722 590 724 627 696 825 677 656 785 412 352 839 729 696 641 695 638 762 635 721 854 418 367 824 687 601 676 740 691 683 594 729 731 386 331 706 715 657 653 642 643 718 654 632 731 392 344 792 852 649 629 685 617 715 715 629 916 531 357 917 828 708 858 775 785 1006 789 734 906 532 387 991 841 892 782 813 793 978 775 797 946 594 438 1022 868 795

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.121313434871579 beta 0 gamma 0.727613202056801 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 614 647.620192307693 -33.6201923076928 14 647 666.82278845398 -19.8227884539805 15 580 581.282528387406 -1.28252838740593 16 614 613.033117619586 0.966882380413608 17 636 637.014923931782 -1.01492393178171 18 388 383.964643846328 4.03535615367218 19 356 400.360363918437 -44.3603639184371 20 639 357.218366288849 281.781633711151 21 753 673.475107980917 79.5248920190827 22 611 712.653722945721 -101.653722945721 23 639 650.144604470535 -11.1446044705352 24 630 565.865458044773 64.1345419552268 25 586 669.890483722475 -83.8904837224753 26 695 691.815904759382 3.18409524061758 27 552 620.920291796552 -68.920291796552 28 619 645.90365877734 -26.9036587773400 29 681 665.237338143583 15.7626618564166 30 421 417.451270613437 3.54872938656263 31 307 402.846445716454 -95.8464457164538 32 754 561.975406134494 192.024593865506 33 690 738.031789830672 -48.0317898306716 34 644 645.900615091595 -1.90061509159455 35 643 653.359345657001 -10.3593456570012 36 608 617.304728146627 -9.3047281466271 37 651 617.781679800204 33.2183201997957 38 691 709.584576940514 -18.5845769405137 39 627 589.948628304088 37.0513716959123 40 634 654.650861703136 -20.6508617031362 41 731 702.021543123609 28.9784568763912 42 475 448.029825309511 26.9701746904890 43 337 372.718633002093 -35.7186330020926 44 803 723.190511083501 79.809488916499 45 722 732.155099517306 -10.1550995173059 46 590 674.11256343875 -84.1125634387495 47 724 666.189841991122 57.8101580088784 48 627 639.079364443766 -12.0793644437661 49 696 666.40656893179 29.5934310682096 50 825 724.649849687071 100.350150312929 51 677 655.012788238624 21.9872117613761 52 656 680.995963101049 -24.9959631010490 53 785 759.569729687146 25.4302703128540 54 412 503.863586117536 -91.8635861175355 55 352 374.056552474132 -22.0565524741315 56 839 800.048029727487 38.9519702725128 57 729 746.537737331535 -17.5377373315350 58 696 640.315331336555 55.6846686634447 59 641 740.089324952775 -99.089324952775 60 695 649.261389180738 45.7386108192617 61 638 710.245940337771 -72.2459403377711 62 762 801.372617178017 -39.3726171780174 63 635 664.684436579969 -29.6844365799691 64 721 654.360737919369 66.639262080631 65 854 776.2907954428 77.7092045571995 66 418 451.935672033139 -33.9356720331388 67 367 373.786776918547 -6.78677691854745 68 824 840.636112721433 -16.6361127214334 69 687 744.265886513551 -57.2658865135514 70 601 680.038224210279 -79.038224210279 71 676 664.514705234317 11.4852947656833 72 740 679.695820229922 60.3041797700785 73 691 667.014662171078 23.9853378289220 74 683 790.832846030486 -107.832846030486 75 594 652.033599524172 -58.0335995241725 76 729 699.854740054528 29.1452599454718 77 731 824.313772088603 -93.313772088603 78 386 407.831788073037 -21.8317880730366 79 331 348.508738408874 -17.5087384088740 80 706 807.760243024426 -101.760243024426 81 715 675.086916307864 39.9130836921358 82 657 608.728356397025 48.2716436029752 83 653 666.524898539208 -13.5248985392084 84 642 709.883999619971 -67.883999619971 85 643 658.431661515548 -15.4316615155482 86 718 693.190876066811 24.8091239331891 87 654 602.321729277115 51.678270722885 88 632 719.189669589688 -87.1896695896876 89 731 751.242271053243 -20.2422710532435 90 392 389.326415494836 2.67358450516389 91 344 335.740112378772 8.25988762122779 92 792 744.25200817518 47.7479918248206 93 852 720.294022610471 131.705977389529 94 649 670.41516860093 -21.4151686009303 95 629 680.24851913296 -51.2485191329597 96 685 684.277076078083 0.7229239219173 97 617 674.682764306154 -57.6827643061538 98 715 730.044054979828 -15.0440549798276 99 715 651.518808479866 63.4811915201341 100 629 681.034224826663 -52.0342248266631 101 916 760.154067953868 155.845932046132 102 531 434.251190655471 96.7488093445294 103 357 395.649045274614 -38.6490452746141 104 917 823.716737627526 93.283262372474 105 828 858.960821867563 -30.9608218675631 106 708 691.451222120707 16.5487778792930 107 858 686.816337372139 171.183662627861 108 775 751.056533756071 23.9434662439289 109 785 706.937862595599 78.0621374044014 110 1006 806.02763420346 199.972365796539 111 789 803.791409161267 -14.7914091612669 112 734 749.957225437861 -15.9572254378614 113 906 966.360612916558 -60.360612916558 114 532 576.445589425618 -44.445589425618 115 387 434.148867993739 -47.1488679937387 116 991 945.535539734794 45.4644602652058 117 841 895.543857846838 -54.5438578468385 118 892 755.54829394039 136.451706059609 119 782 864.324122550107 -82.324122550107 120 813 803.673290690838 9.32670930916152 121 793 792.38185527175 0.618144728250172 122 978 960.019196505357 17.9808034946434 123 775 798.397030742782 -23.3970307427824 124 797 742.773511928395 54.2264880716049 125 946 939.302089831546 6.6979101684542 126 594 567.697340021025 26.3026599789748 127 438 432.255006950696 5.74499304930379 128 1022 1009.27018533099 12.7298146690063 129 868 891.36763848615 -23.3676384861495 130 795 877.266026191264 -82.2660261912636 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 131 819.635454044015 689.008340930445 950.262567157586 132 827.568048691115 695.983230021659 959.15286736057 133 809.577390092995 677.041786091045 942.112994094944 134 988.240452822233 854.760835831288 1121.72006981318 135 797.982306238411 663.565305915024 932.399306561798 136 794.825288352778 659.477396607744 930.17318009781 137 954.388356217866 818.115931921117 1090.66078051461 138 594.505238007991 457.314511471533 731.695964544449 139 442.728619029250 304.625696281435 580.831541777066 140 1023.51255598068 884.503422844126 1162.52168911724 141 880.987023479102 741.077549463706 1020.8964974945 142 832.063892109122 691.259834130835 972.86795008741

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293537462ypx8bhbmhfvwhta/13pct1293537588.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293537462ypx8bhbmhfvwhta/13pct1293537588.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293537462ypx8bhbmhfvwhta/23pct1293537588.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293537462ypx8bhbmhfvwhta/23pct1293537588.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293537462ypx8bhbmhfvwhta/3wzbe1293537588.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293537462ypx8bhbmhfvwhta/3wzbe1293537588.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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